Folding transition of a single semiflexible polyelectrolyte chain through toroidal bundling of loop structures.

We consider how the DNA coil-globule transition progresses via the formation of a toroidal ring structure. We formulate a theoretical model of this transition as a phenomenon in which an unstable single loop generated as a result of thermal fluctuation is stabilized through association with other loops along a polyelectrolyte chain. An essential property of the chain under consideration is that it follows a wormlike chain model. A toroidal bundle of loop structures is characterized by a radius and a winding number. The statistical properties of such a chain are discussed in terms of the free energy as a function of the fraction of unfolded segments. We also present an actual experimental observation of the coil-globule transition of single giant DNA molecules, T4 DNA (165.5 kbp), with spermidine (3+), where intrachain phase segregation appears at a NaCl concentration of more than 10 mM. Both the theory and experiments lead to two important points. First, the transition from a partially folded state to a completely folded state has the characteristics of a continuous transition, while the transition from an unfolded state to a folded state has the characteristics of a first-order phase transition. Second, the appearance of a partially folded structure requires a folded structure to be less densely packed than in the fully folded compact state.